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Full text of "History Of The Theory Of Numbers - I"

CHAP. XVI] FACTOBS OF an =*=&*. 391 A. Cunningham86 tabulated factors of yv=*= 1, x™ =t y*", and gave an account of printed and manuscript tables of solutions of ym=*=lzzQ (mod pk). Cunningham87 tabulated factors of xy**y* for #g!6 and certain y's as high as 31 when #=2 or 4, where x, y are relatively prime and x> 1, y> 1. Cunningham88 noted that x-2*+l is composite for l<o;<233, X5^141. A. Cunningham and H. J. Woodall89 tabulated factors of 2a=*=g and g.2a=±=l for #^566, and tabulated values of q for which one of these four functions is divisible by a given prime p or power of p. They confirmed that x.2x+1 is composite when 1< x < 233 except perhaps when x = 141. Incidentally (p. 15), the factors of 2*=*= k—1 for k£ 17 are given. For factors of 2n—1 and 10n—l, see Chapters I and VI. For factor tables of numbers w.2*=»=l, see Seelhoff72 and Morehead90 of Ch. XIII; for m.6k=±I, Dines91. For factors of several numbers an—1, see Lawrence15, Biddle16, and Kraitchik21 of Ch. XIV. For the form of factors of a*+6* when & = 2n, see Euler11 of Ch. XV. Various results in Ch. XVII relate to factors of an =*=&". FACTORS OP TRINOMIALS. Seven96 primes p such that (p2 — !)2 has 4 or more factors px+1, x<p. List96 of algebraically factorable trinomials x5+xy*+y5, etc. Factors97 of 148+145+1, 78+2-75+l, etc. Conditions that.z8+Pz4+c8 be a product of 4 rational quadratic factors.98 Two99 factors of x«+(4m*+8m*+2)x*tf+y*. Factors100 of various trinomial expressions. For factors of 34+66x24-&2 see Dirichlet9 of Ch. XVII. See papers 28, 28a, 65, 89 above. "Messenger Math., 45, 1915, 49-75. *Vbid., 185-192. 88Proc. London Math. Soc., (2), 4, 1907, xviii; (2), 15, 1916-7, xxix. "Messenger Math., 47, 1917, 1-38. Math. Quest. Educ. Times, (2), 10, 1906, 44. MMath. Quest. Educat. Times, (2), 15, 1909, 82-3. Amer. Math. Monthly, 15, 1908, 67, 138. L'interme'diaire dea math., 15, 1908, 121. "Math. Quest. Educ. Times, (2), 16, 1909, 39-41. "Ibid., 65-6. >*Ibid., (2), 18, 1910, 64-5; (2), 22, 1912, 20-1. "Sphinx-Oedipe, 6, 1911, 8-9. 10°Math. Quest. Educ. Times, 72, 1900, 26-8; 74, 1901, 130-1; (2), 6, 1904, 97; 19, 1911, 85; 20, 1911, 25-6, 76-8; 22, 1912, 54-61. Math. Quest, and Solutions, 3, 1917, 66; 4,1917, 13, 39; 5, 1918, 38, 50-1.